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Research Designs for Causal Inference Department of Political - PowerPoint PPT Presentation

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Background IV RDD ITS DID Research Designs for Causal Inference Department of Political Science and Government Aarhus University March 10, 2015 Background IV RDD ITS DID 1 Background 2 Instrumental Variables 3 Regression Discontinuity

  1. Background IV RDD ITS DID Finding Instruments Forward, not backward, causal inference Most instruments are not things we care about Weather, disasters Geography, borders, climate Lotteries A good instrument is one that satisfies both of our conditions, so we need: A good story about exogeneity Evidence that instrument is strong

  2. Background IV RDD ITS DID Instrumental Variables Activity Read each scenario Assess exogeneity and relevance Discuss with the person sitting next to you

  3. Background IV RDD ITS DID Questions about IV?

  4. Background IV RDD ITS DID 1 Background 2 Instrumental Variables 3 Regression Discontinuity Designs 4 Interrupted Time-Series 5 Difference-In-Differences

  5. Background IV RDD ITS DID Example: Maimonides’ Rule

  6. Background IV RDD ITS DID Example: Maimonides’ Rule 1 What is Maimonides’ Rule?

  7. Background IV RDD ITS DID Example: Maimonides’ Rule 1 What is Maimonides’ Rule? 2 Why is it a valid (credible) instrument? (Or why isn’t it?)

  8. Background IV RDD ITS DID Example: Maimonides’ Rule 1 What is Maimonides’ Rule? 2 Why is it a valid (credible) instrument? (Or why isn’t it?) 3 How does it differ from a randomized experiment?

  9. Background IV RDD ITS DID Z Class Size Test Scores Grade Size

  10. Background IV RDD ITS DID How RDD Works 1 Find a consequential threshold Examples? 2 Causal inference is about comparisons In an experiment, X is randomly assigned In matching or regression, we compare units that differ only in X but are similar in Z 3 In RDD, X is not randomly assigned and there is no covariate overlap W causally determines X , so units with different values of X also differ in their value of W compare units that are as similar as possible

  11. Background IV RDD ITS DID Regression Discontinuity Y X

  12. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X

  13. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X

  14. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  15. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  16. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  17. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  18. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  19. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  20. Background IV RDD ITS DID Regression Discontinuity Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  21. Background IV RDD ITS DID Is There A Discontinuity? Y X

  22. Background IV RDD ITS DID Is There A Discontinuity? • • Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X

  23. Background IV RDD ITS DID Is There A Discontinuity? • • Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  24. Background IV RDD ITS DID Is There A Discontinuity? • • Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  25. Background IV RDD ITS DID Is There A Discontinuity? • • Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  26. Background IV RDD ITS DID Is There A Discontinuity? • • Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  27. Background IV RDD ITS DID “Sharp” and “Fuzzy” RDD If a threshold perfectly causes X , then it produces a sharp discontinuity Potentially analyze as an experiment

  28. Background IV RDD ITS DID “Sharp” and “Fuzzy” RDD If a threshold perfectly causes X , then it produces a sharp discontinuity Potentially analyze as an experiment If a threshold imperfectly (probabilistically) causes X , then it produces a fuzzy discontinuity  1 , if X > threshold   W = 0 , if X < threshold  

  29. Background IV RDD ITS DID “Sharp” and “Fuzzy” RDD If a threshold perfectly causes X , then it produces a sharp discontinuity Potentially analyze as an experiment If a threshold imperfectly (probabilistically) causes X , then it produces a fuzzy discontinuity Analyze using Instrumental Variables  1 , if X > threshold   W = 0 , if X < threshold   Examples?

  30. Background IV RDD ITS DID Sharp vs. Fuzzy RDD Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  31. Background IV RDD ITS DID Sharp vs. Fuzzy RDD Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  32. Background IV RDD ITS DID Modelling RDD Sharp: Treat threshold as an experiment Fuzzy: Treat the threshold as an instrument Not all cases above threshold are treated Not all cases below threshold are untreated Effect is estimated at point of discontinuity, which may not reflect effect X → Y over the entire domain of X Need to choose bandwidths

  33. Background IV RDD ITS DID Sharp vs. Fuzzy RDD Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  34. Background IV RDD ITS DID Sharp vs. Fuzzy RDD Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  35. Background IV RDD ITS DID Sharp vs. Fuzzy RDD Y • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • X Intervention

  36. Background IV RDD ITS DID Modelling RDD Use bandwidths to subset the data Regress Y on X , interacted with W Often use polynomial terms: Y = β 0 + β 1 X + β 2 X 2 + ... + β 3 Z + β 4 XZ + β 5 X 2 Z + ...

  37. Background IV RDD ITS DID Problems with Discontinuities Campbell’s Law : The more any quantitative social indicator (or even some qualitative indicator) is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor.

  38. Background IV RDD ITS DID Problems with Discontinuities Campbell’s Law : The more any quantitative social indicator (or even some qualitative indicator) is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor. Discontinuities are exploitable

  39. Background IV RDD ITS DID Problems with Discontinuities Campbell’s Law : The more any quantitative social indicator (or even some qualitative indicator) is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor. Discontinuities are exploitable Compensatory rivalry and equalization

  40. Background IV RDD ITS DID Questions about RDD?

  41. Background IV RDD ITS DID 1 Background 2 Instrumental Variables 3 Regression Discontinuity Designs 4 Interrupted Time-Series 5 Difference-In-Differences

  42. Background IV RDD ITS DID How ITS Works Identify an exogenous shock in X that might affect Y Look at Y before ( t ) and after ( t + 1) the shock We only observe one manifest outcome at each point in time

  43. Background IV RDD ITS DID time Intervention

  44. Background IV RDD ITS DID time Intervention

  45. Background IV RDD ITS DID How ITS Works Identify an exogenous shock in X that might affect Y Look at Y before ( t ) and after ( t + 1) the shock We only observe one manifest outcome at each point in time

  46. Background IV RDD ITS DID How ITS Works Identify an exogenous shock in X that might affect Y Look at Y before ( t ) and after ( t + 1) the shock We only observe one manifest outcome at each point in time To make a causal inference, we need: Y 0 , t and Y 1 , t , or Y 0 , t + 1 and Y 1 , t + 1 Use pre-post comparisons to infer the value of unobserved potential outcomes

  47. Background IV RDD ITS DID time Intervention

  48. Background IV RDD ITS DID • • time Intervention

  49. Background IV RDD ITS DID • • time Intervention

  50. Background IV RDD ITS DID • Effect? • time Intervention

  51. Background IV RDD ITS DID • Effect? • time Intervention

  52. Background IV RDD ITS DID • • time Intervention

  53. Background IV RDD ITS DID Effect? • • time Intervention

  54. Background IV RDD ITS DID Threats to Inference Campbell and Ross talk about six “threats to validity” (i.e., threats to causal inference) related to time-series analysis What are those threats?

  55. Background IV RDD ITS DID ITS Considerations Changes in level and/or slope Effects can be delayed

  56. Background IV RDD ITS DID time Intervention

  57. Background IV RDD ITS DID ITS Considerations Changes in level and/or slope Effects can be delayed

  58. Background IV RDD ITS DID ITS Considerations Changes in level and/or slope Effects can be delayed Improving the design (easiest to hardest):

  59. Background IV RDD ITS DID ITS Considerations Changes in level and/or slope Effects can be delayed Improving the design (easiest to hardest): Multiple outcome measures

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